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Q: Fachverband Quantenoptik und Photonik
Q 7: Quantum Information: Concepts and Methods 1
Q 7.5: Vortrag
Montag, 14. März 2011, 11:30–11:45, SCH A118
Quantification of entanglement and polynomial invariants of homogeneous degree 4 — Christopher Eltschka1, Thierry Bastin2, Andreas Osterloh3, and •Jens Siewert4, 5 — 1Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany — 2Institut de Physique Nucléaire, atomique et de Spectrosopie, Université de Liège, 4000 Liège, Belgium — 3Fakultät für Physik, Universität Duisburg-Essen, 47048 Duisburg, Germany — 4Departamento de Química Física, Universidad del País Vasco, 48080 Bilbao, Spain — 5Ikerbasque, Basque Foundation for Science, 48011 Bilbao, Spain
The N-tangle of Wong and Christensen [1] (which for N=3 is the three-tangle) gives the simplest SL(2,C)⊗ N-invariant polynomial of homogeneous degree 4. The relevance of degree-4 polynomials for entanglement classification and quantification is increasing with the possibility of polynomial SLOCC classifications [2]. Extending a well-known theorem [3] we prove that all such polynomials naturally lead to degree-4 entanglement monotones. By focusing on four qubits we show how various degree-4 polynomial invariants introduced by different authors can be put into a common framework. Surprisingly, the invariants defined by Luque and Thibon [4] have a precise physical meaning, and have generalizations to multi-qubit and even multi-qudit systems.
[1] A. Wong and N. Christensen, Phys. Rev. A 63, 044301 (2001).
[2] O. Viehmann, C. Eltschka, and J. Siewert, unpublished.
[3] F. Verstraete et al., Phys. Rev. A 68, 012103 (2003).
[4] J.-G. Luque and J.-Y. Thibon, Phys. Rev. A 67, 042303 (2003).